A rail gun uses electromagnetic forces to accelerate a projectile to very high v
ID: 1385379 • Letter: A
Question
A rail gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and can be illustrated in the following example. A metal rod of mass 30.0g and electrical resistance 0.200? rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 10.0cm apart. (Figure 1) The rails are also connected to a voltage source providing a voltage of V = 5.00V
Part A
Find ?s , the coefficient of static friction between the rod and the rails.
Give your answer numerically.
.
Explanation / Answer
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A rail gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and can be illustrated in the following example. A metal rod of mass 50.0 g and electrical resistance 0.300 Omega rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 7.00 cm apart. The rails are also connected to a voltage source providing a voltage of V = 5.00 V.
The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value B = 0.210 T. Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s^2 for the magnitude of the acceleration due to gravity.
Find mu_s, the coefficient of static friction between the rod and the rails.
Answer
Given that
Mass of rod m = 50.0 x 10^-3 kg
resistance R = 0.30 ?
acceleration due to gravity g =9.80 m/s2
Length L = 7.00 x 10^-2 m
voltage V= 5.00 V
Magnetic field B= 0.210 T
-------------------------------------------------------
The current I = V/R
= (5.00 V)/(0.3 ?)
= 16.67 A
The frictional force is = BIL
?mg = BIL
? = (BIL)/(mg)
= (0.210 T)(16.67 A)( 7.00 x 10^-2 m)/((50.0 x 10^-3 kg)(9.80 m/s2))
= 0.5001
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